Is Energy Conserved in General Relativity?

  • Thread starter Thread starter zaybu
  • Start date Start date
  • Tags Tags
    Energy
AI Thread Summary
In general relativity (GR), energy conservation is defined locally rather than globally, leading to the conclusion that energy can appear to increase with the universe's expansion and the constant density of dark energy. The discussion highlights that while energy is conserved in closed systems, GR lacks a global conservation law due to the failure of Gauss's law in four-dimensional space. This means that the universe can theoretically create or annihilate energy, complicating traditional energy calculations. Additionally, the energy density associated with the cosmological constant remains constant, while the volume of space expands, resulting in an overall increase in total energy. Ultimately, GR does not provide a framework for global energy conservation, particularly in dynamic cosmological contexts.
zaybu
Messages
53
Reaction score
2
It seems that energy is conserved only locally. Globally, with the expansion of the universe and Dark energy density being always constant, it means that energy is increasing. Can anyone clarify this?

Thanks.
 
Physics news on Phys.org
zaybu said:
Globally, with the expansion of the universe and Dark energy density being always constant, it means that energy is increasing.

Does it really? Why would that be?
 
JaredJames said:
Does it really? Why would that be?
LOL...that is funny :)

zaybu,
Yes, energy into any closed system will always equal energy out of that closed system.

Until someone actually shows us a jam-jar full of dark energy, you can take it that it won't effect any energy calculations you will have to do in your lifetime.

John.
 
It is indeed conserved locally. If you are talking in terms of GR (and I assume you are) then global energy conservation is impossible to define in general. It can really only be defined globally in space - times where there are respective global symmetries.
 
I'm told by those who know more than I do about it (on these forums) that GR doesn't conserve energy globally. It has something to do with Gauss's law failing in 4-space.

Apparently there is no problem in GR for the universe to manufacture new energy or annihilate energy.
 
Antiphon said:
I'm told by those who know more than I do about it (on these forums) that GR doesn't conserve energy globally. It has something to do with Gauss's law failing in 4-space.

Apparently there is no problem in GR for the universe to manufacture new energy or annihilate energy.

Is this related to how redshifted light could conserve energy?
 
Antiphon said:
I'm told by those who know more than I do about it (on these forums) that GR doesn't conserve energy globally. It has something to do with Gauss's law failing in 4-space.

Apparently there is no problem in GR for the universe to manufacture new energy or annihilate energy.

Yes, this is what I'm talking about. According to GR, energy is not conserved. Krauss has said that the sum is zero. I'm not sure to what he's referring. How does gravitational waves fit in that picture?

Thanks
 
I was under the impression that energy density of the universe is changing, but that total energy is not.

It was the steady state universe theories, no longer supported by scientific consensus, that required the constant creation of energy to maintain a steady state.
 
Last edited:
JaredJames said:
Does it really? Why would that be?

Photons with wavelength "L" and energy "E" become photons with wavelength "K.L" and energy "E/K" if the Universe expands by a factor of "K". So the energy of radiation will go down as "1/K".

On the contrary, the energy stored e.g. in the cosmological constant will expand as "K^3". Why? Well, the energy density carried by the cosmological constant is constant during the cosmological evolution - that's why the "cosmological constant" is called a "cosmological constant". ;-) But the volume of space is literally expanding so the total energy is increasing proportionally to the volume.


So the conventional formulae for the energy of objects propagating upon the background geometry explicitly lead to non-conserved quantities and we can see that they're not conserved. Only the dust (with no pressure) would conserve the energy ("E=mc^2") in an expanding Universe but no physical evolution will guarantee that everything stays in the form of "exact dust".
 
  • #10
zaybu said:
Yes, this is what I'm talking about. According to GR, energy is not conserved. Krauss has said that the sum is zero. I'm not sure to what he's referring. How does gravitational waves fit in that picture?

Thanks

Gr doesn't say that energy is not conserved. It just has no general global conservation laws. Usually only in the case where space - time has time - like killing vectors can one say there is global energy conservation in that space - time. Gravitational Waves carry energy away from a radiating system and one can define the energy flux of a gravitational wave based upon conservation of energy so that there is no net change in energy but again global energy conservation is not concrete in GR .
 

Similar threads

I Mechanism of Energy Conservation in Zero-Amplitude Sum of EM Waveforms
Replies
12
Views
694
B Conservation of kinetic energy in expanding space
Replies
25
Views
388
I Energy conservation in general relativity
Replies
12
Views
3K
A A global energy conservation law in general relativity
Replies
36
Views
517
I Dark energy and conservation of energy
Replies
4
Views
1K
I Conservation of stress-energy tensor
Replies
19
Views
1K
A Does Spacetime Absorb Energy in General Relativity?
Replies
17
Views
2K
I Voids, dark energy and tidal forces...?
Replies
0
Views
2K
I Source of Energy in a Field of Forces
Replies
4
Views
2K
I Is conservation of energy a local law in Quantum field theory?
Replies
18
Views
2K

Hot Threads

Recent Insights

Back
Top